The accomplished graphics team at NYT outdid themselves with this feature on the 100m dash through Olympic history (link). You should really go and check out the full presentation.

***

They start with a data table like the one shown on the right. It's a boring list of names and winning times by year and by medal type. What can one do to animate this data? The NYT team found many ways.

They found many ways to convey the meaning of the tenths and hundredths of a second that separate the top performers. In the dot plot, for example, they did not draw the actual winning times. Instead, they converted the differences in winning times into distances. Here is the right section of the chart:

We are drawn into compressing time and place, having Usain Bolt race all of the former winners and assuming everyone ran the same race they did in real life. The dot plot tells us how far ahead of each past winner Bolt is.

Some time ago, I wrote about the "audiolization" of duration data, in another piece about a NYT chart (link). They deployed this strategy beautifully at the end of the short film. The runners were aligned like keys on a piano, and the resulting sound is like playing a scale across the keyboard. Lovely, that is to say.

***

The authors bring in a number of other data points to create reference points for understanding this data. For example, if you blink, you might miss the national jerseys worn by each winner in the hypothetical competition:

Later, the dominance of American runners is plainly shown via white lanes:

The perspective hides the relative impotency of American sprinters in recent Olympics. This view of the surge of Caribbean runners makes up for it:

***

Next, they compared the times for U.S. age group record holders to Olympic winning times. This is a fun way to look at the data. (Pardon the strutting Play button.)

They play with foreground/background here in an effective way. The 15- and 16-year-old age-group record holder is said to be "good enough for a bronze as recently as 1980".

Fun aside, think twice before you repeat this "insight". It falls into the category of those things that sound impressive but are quite meaningless. For one thing, the gap between the two runners is affected by a multitude of factors: the age of the runner (which is elevated here over and above other factors), the nationality of the runner, and the time of the run. This last point is key: if we compare the 15-to-16-year-old 100m record time from 1980 to the winning times of Olympic medalists from that year, the gap would be much wider.

Also, pay attention to the distribution of runners. It gets very crowded very quickly near the top end of the scale. In other words, while the gap as measured in part-seconds may seem small, the gap as measured in individual athletes would be very wide -- we'd find loads of athletes whose times fit into the gap illustrated here.

***

According to the dot plot, in some years, like the 1950s, there were no gold medalists. Looking at the data here, I think this is an overplotting effect, where two times were so close that the dots were literally on top of each other. This creates the situation where one of the dots will be on top of the other, and which one is on top is a feature of the software you're using. Jittering is one common strategy to deal with this problem, or we can just place the gold, silver and bronze dots on their own levels. The latter strategy would look exactly like the over-the-top view used in the short film:

(We'll also note that this view has time running left to right, which is perhaps more natural than time running bottom up, as in the dot plot. However, we are used to seeing runners cross the finish line from left to right on a TV screen so this is a case of eight ounces and half a pound.)

In the short film, I find the gigantic play/pause button at the center of the screen an annoyance, ruining my enjoyment. (I'm using Firefox and a Mac.)

The New York Times (link) uses two histograms to show us the geographical distribution of college graduates today compared to 1970. The histograms clearly and forcefully demonstrate two points: the almost three-fold increase in the concentration of college graduates in metropolitan areas, and the wider spread in geographical preference. In other words, we find that the shape of the distribution (in particular, the width) and the mid-point of the distribution have both shifted in those decades.

Readers must be careful about interpreting the colors, which are keyed to relative scales. Every single orange square on the right chart represent a higher percentage of college graduates than the single orange square on the left... this is because of the massive increase in the number of adults with college degrees over this period of time.

I'd suggest two small improvements. Arranging the histograms vertially makes a huge difference:

On the maps, I'd get rid of the gray dots. The point of the maps is to show where the graduates are flocking to and where they are not favoring. The gray dots on the other hand serve mainly as a geographical lesson of where the metropolitan areas are on the U.S. map.

The New York Times chose to present the poll results from Super Tuesday in the following chart (link):

It took me a bit of time to take in what this chart has to offer. To save your troubles, I've drawn up a reader's guide:

The graphic is a disguised scatter plot with one axis being Romney's share minus Santorum's share and the other axis being the total share of all other candidates. This is an "uneven canvass" in the sense that the data are much more likely to fall into a small part of the chart area (the orange shaded region).

If the reader just wants to know which segments of the electorate favors Romney v. Santorum, the chart is pretty effective at pointing to the answer. It is quite challenging to learn much else about the data.

***

Here are the results for Ohio, plotted as a stacked bar chart, with three segments in each bar (Romney's share, Santorum's share and the share of all other candidates).

This more standard presentation conveys much more of the underlying information. The trade-off is that the reader has to try harder to figure out the answer for each segment of voters.

[PS: 3/13/2012]:

Thanks to several readers for your comments. I went back to look at the NYT graphic again, and can confirm that it is a ternary chart. The chart area is indeed an equilateral triangle with three equal sides.

What threw me off was the axis labels, particularly the Santorum and Romney labels which give the impression that there is a zero mid-point and some kind of share data along the east-west axis. If this were true, then the chart could not be a ternary plot because Romney and Santorum shares are not mirror images.

In a ternary plot, we must identify Romney, Santorum, and "Other candidates" as the three vertices. The way this chart is labelled, it invites readers to drop a perpendicular line to the horizontal axis to read Santorum's share (e.g.). That doesn't work. Trying to fish the data out of a ternary plot is always challenging. You pick the vertex corresponding to the data series you want, say Romney's share. Then you take the side opposite that vertex. Now draw lines parallel to that side -- as you approach the Romney vertex, Romney's share goes from 0% to 100%. The following chart shows this:

For ternary plots, it's easier to go with the hand-waving principle that the closer you are to the vertex, the greater the weight of that vertex. So with the abortion data point, we see that it is much closer to the Santorum corner than the other two corners.

The vertical line for "other candidates" is also misleading. To read the share of votes that went to other candidates, one has to followS either the OR side or the SO side of the triangle. Basic geometry will show that going up the vertical line will not produce the share of "other candidates".

***

Lastly, here is a scatter plot representation of the data using the Romney-Santorum difference as the horizontal axis and the share of all others as the "other candidates":

The pattern of dots on this chart looks very similar to the ternary chart (that is one other reason why I thought the original graphic was a scatter plot.) However, the two plots are distinct entities. For the scatter plot, the horizontal axis goes from -100% to +100% while the vertical axis can only go from 0% to 100%.

The main idea is that there are people who will pay more taxes and those who will pay less under every income group. The impact of the tax policy depends on the mix between those paying more and those paying less.

The data table is far too cumbersome to bring out the message. Here is a visualization:

For example, for the top 20% income group, about 50 % will see an average tax cut of 3900. But about 80 to 90% of the other 4 quintiles will experience tax hikes.

The New York Times Magazine published an article about marriage infidelities, which I didn't read, but it was popular enough that they did an online poll to obtain some instant feedback from readers. The result was shown in this cutesy graphic:

Note that they plotted the number of responses rather than proportion of responders even though all the numbers are between 0 and 100 and could easily have been misread as percentages.

This chart is another good illustration of the self-sufficiency principle. There is no need to create a chart if all the data are printed onto the chart, and readers must look at the data to learn anything from it. Imagine the above chart without the data, and you'll see why the data labels are critical to this chart.

Below is a version in which I removed all the data labels, replacing them with an axis:

The two pink slabs were thrown in for a little chart-check. According to the designer, 6+6+6 is larger than 20. How is this so? Look at a blow-up of the "God says otherwise" bar of hearts:

The one whole heart in each bar ruins the string of half hearts. Little things can introduce infidelities into charts.

Andrew Gelman has posted a few times recently on graphics-related topics. Here are the links, and my reaction:

He and I both think line charts are under-valued. Some people really, really hate using line charts when the horizontal axis consists of categorical data; as I've explained repeatedly (see posts on profile charts), by drawing lines to connect these categories, all I'm doing is to expose our eye movements while reading the bar charts that are often the default option for such data.

Regarding a very "ugly" chart on factors affecting military spending, Gelman wrote the following spot-on sentences:

Just as a lot of writing is done by people without good command of the tools of the written language, so are many graphs made by people who can only clumsily handle the tools of graphics. The problem is made worse, I believe, because I don't think the creators of the graph thought hard about what their goals were.

That last point is exactly why I placed at the top of the Trifecta checkup the question of figuring out what is the key question the chart is supposed to address.

Seems to me the above chart presents in a complicated fashion a simplistic model of military spending share: military spend = military share of GDP x GDP, therefore relative military spend increases if either relative GDP increases or relative military share of GDP increases (or both). So, in each period, all we need to know is whether the US has increased/decreased its military share of GDP relative to the rest of the world, and whether the US has increased/decreased its GDP relative to the rest of the world. End of story.

Some work on visually displaying telephone call data. Gelman's correspondent nominated this and another chart printed in the NYT as worst of the year. Chris Volinsky disagrees and points us to a nice article. The map shown here is definitely not close to being worst of the year. The other chart, with a lot of lines, is pretty bad - and raises the question I asked the other day: what makes a "pretty" chart?

Regarding the AT&T analysis, I have a few questions for the researchers: how representative is AT&T data especially at county level? do we have to worry about nonrandom missing data? Also, how should one interpret the large swath of the Midwest which had the "background color"? Is it that there weren't sufficient data or that the data showed that all of those states belong together in one super-cluster? Finally, how does a shift in the "similarity" metric change the look of the map?

Based on the evidence out there, it would seem like "pretty" means one or more of the following:

unusual: not your Grandma's bar chart or line chart

visually appealing: say, have irregular shapes, lots of colors, curved lines and so on

complex: if you don't get the point right away, the chart must be smart, and must contain a lot of information

data-rich: a variant of complex

***

I pondered that question while staring at this chart, reprinted in the NYT Magazine, in which they pitched a new book by Craig Robinson called "Fip Flop Fly Ball". According to the editors, the book is a "beautiful, number-crunched (sic) combination of statistical and graphic-design geekery". So here's Exhibit A:

This chart is supposed to tell us whether big payroll equals success in Major League Baseball, and success is measured variously by making the playoffs, making the championship series or winning the championship. It nicely uses a relatively long time horizon of 15 years.

The problem: how are we supposed to learn the answer to the question?

To learn it, we have to go through these steps:

Read the fine print under the title that tells us the vertical scale is the rank by payroll, so within each season, the top spender is at the top, and the bottom spender at the bottom. (Strictly speaking, there are 15 different scales, see discussion below.)

Figure out that the black row has all of the championship teams aligned at the same vertical level.

Realize that the more teams that are listed below the black line, the bigger the payroll of the championship team in that season.

Alternatively, the more teams that are found above the black line, the smaller the payroll is of the winning team that year.

From that, we see that for almost every season in the last 15 years, the winner comes from a relatively free-spending team. Florida in 2003 is a big outlier.

***

Maybe that isn't too bad. Now, try to interpret the blue boxes, which label all the playoff teams in every season. Is it that playoff teams also are bigger spenders than non-playoff teams?

To learn this, try the following step:

Ignore the relative height of the columns from season to season, and focus only on the relative positions of the blue slots within each column.

Are these blue slots more likely to be crowded towards the top of the column than the bottom?

The answer should be obvious but why does it feel so hard?

***

You may be confused by the vertical scale. Is it the case that in 2003, the entire league decided to splurge on spending? Does the protruding tower in 2003 indicate especially high payrolls?

No, it doesn't. It turns out there are really 15 separate vertical scales on this one chart; each column has to be viewed separately. There is a ranking within each column but the relative height from one column to the next means nothing. Each column is hinged to the black row which is the rank by payroll of the championship team in that season.

The decision to anchor the columns in this way is what dooms this chart. In the junkart version below, I reversed this decision and ended up with a much clearer picture:

It's now clear that almost all the playoff teams come from the top quartile or top third of the table in terms of payroll. In more recent years, the correlation between spending and success seems less assured - perhaps it's partly a result of the analytics revolution, as nicely portrayed in Moneyball. It is still true that any team in the bottom third of the payroll scale has little chance to making the playoffs; however, once the smaller-payroll team makes the playoffs, it appears that they do well, as in three of the last four seasons, a small-payroll team has made the finals.

Note that I grayed out the four cells at the bottom left. There were only 28 teams before 1997. I also removed the names of the teams that didn't make the playoffs, which serves no purpose in a chart like this.

***

That's the descriptive statistics. It's really hard to draw robust conclusions from such data. You can say it's harder for small-payroll teams to have consistently great performance in the regular season but easier in a short playoff series - so in a sense, we are looking at luck, not skill.

But could it be that those small-payroll teams, given that they made the playoffs, must have some usual success in that season, perhaps because they discovered some young talent that cost next to nothing, and so the fact that they made the playoffs despite the smaller payroll is a good predictor that they would do well in the playoff?

The other important issue to realize is that by plotting the rank of payroll, rather than true payroll, the scale of payroll differences has been taken out of the picture. The team listed at the median rank most likely spent much less than half of the team listed at the top of the table. If you grab the actual payroll amounts, there is much more you can do to display this data.

Felix Salmon, a blogger and foodie, investigated whether a restaurant changes its pricing based on the number of stars it gets from Sam Sifton, the New York Times' food critic. His conclusion is that "price hikes happen all over the place, from the worst-reviewed restaurants to the best." This plot was used in the post.

His message doesn't jump out of his chart. We would have to recognize that it's the dark green pieces we should be focused on, and it's the relative heights of these pieces within each stacked column. I was also misdirected by the two axis labels: number of stars and number of reviews aren't the primary dimensions. So, I thought one could find a better alternative.

***

This data turn out to be harder to plot than expected. The problem is that the sample size is small, and because of this, the data have ragged edges. We are better at reading patterns from smooth objects.

Here is what I ended up with, a small multiples chart with grouped columns. I adopted Felix's color scheme although no differentiation of color is really necessary in this version. Relative percentages are plotted instead of raw number of reviews. Each set of four columns can be viewed as a histogram or probability distribution. (Again, with more samples, the histograms will look smoother, revealing the pattern more clearly.)

I agree with Felix that there is not much correlation between star rating and pricing. However, this applies truly only to the middle three categories. At the edges, there are a couple of observations: all of the 4-star restaurants hiked their prices while the only restaurant that closed since it got reviewed received zero stars.

I'm a fan of annotating charts and so I'd recommend sticking a note on the 4 stars column, another note on the single gray column, and a third note bracketing the middle three categories, telling readers that there is nothing to see here.

It must be a slow news day when the media spends hundreds of words on discussing a chart that has yet to be unveiled. But the New York Times writer surely got it right with the opener: "Whatever you do, don't call it a pie chart."

We are being told that the government will replace the "food pyramid" with a food pie chart although they will call it something else. This thing which is not a pie chart has not been revealed yet but because chart purists have such political clout it was thought necessary to release a trial balloon on a holiday weekend to gauge what the response might be.

I think we should reserve our judgment till we see this thing.

***

In any case, the focus on encouraging people to eat the right proportions of foods is wrong-headed. Firstly, it is next to impossible for anyone to keep track of the distribution of foods consumed in any given day, unless you keep a diary. Secondly, nutritionists know that the biggest contributor to obesity is the quantity of food being eaten. Thus, a much more effective way is encouraging smaller portions, or knowing when to stop eating. This method also happens to be much easier to put into practice.

This chart highlighted by the Economix blog at the New York Times caught a bit of attention.

Catherine Rampell wrote "awesome chart" on the margin of Branko Milanovic's book which first published this, also conceding that it is a chart that can "take a few minutes" to understand, "but trust me, it's worth it".

The question for me is: is the reward worth the effort?

***

The answer is no. This chart does not address an interesting question, and it tempts readers to infer things that the chart doesn't say.

The message of this data is that there are rich people (by world standard) in poor countries. For me, this isn't very interesting but I can understand if others find it shocking, edifying or even satisfying.

I'd point you to a different visualization, done by the now-famous Hans Rosling, years ago (I discussed his team's work here). If he used lines instead of areas for the distributions, the chart would be even better.

I much prefer this chart.

Comparing the two also surfaces another difference. The four countries chosen in the Milanovic chart are highly selective. (I snicker at the title which announces "Inequality in the world".) It's comparing the U.S. against three developing nations with high income inequality. What about showing us also a few lines of nations with lower inequality, like Scandinavian countries?

***Rampell's conclusions, in particular, are not well supported by her beloved chart. First, she said:

All people born in rich countries thus receive a location premium or a location rent; all those born in poor countries get a location penalty.

I don't disagree that it's better to be born with money. But my takeaway from the chart is the opposite of hers: that you can't generalize entire countries; that you can live in a poor country, and you can be extremely rich. As Rampell pointed out earlier in the article, "[Brazil] this one country covers a very broad span of income groups". So, if anything, the chart undermines the point that "all people" in any one country receive a location premium/rent.

She also said the following:

How can there be so many people in the world who make less than America's poorest, many of whom make nothing each year? Remember that we're looking at the entire bottom chunk of Americans, some of whom make as much as $6700; that may be extremely poor by American standards, but that amounts to a relatively good standard of living in India, where about a quarter of the population lives on $1 a day.

Given that the data has been adjusted for PPP, or in Rampell's words, different costs of living around the world, or really, it has been adjusted for different standards of living, it makes little sense to explain a difference in the adjusted amounts based on "standard of living". In fact, my understanding (unless something changed recently) is that the PPP adjustment uses the US living standard as the reference level.

The $6700 that she describes as the maximum income of the bottom chunk of Americans--if this amount is earned by the Indian, would put him/her in the very top bucket of Indians, according to the Milanovic chart. I'd call that a super high standard of living in India, not merely "relatively good".

***

A few comments on the statistics.

The last quotation above shows a confusion between averages and extreme values. The $6,700 is the maximum income of the bottom chunk of Americans; it cannot be compared to the $1 a day, which by the way, should be written as $365 a year, but in any case, this amount is the average income of the bottom 25% of Indians. One can't compare an average to a maximum, nor an annual number to a daily number.

A number of readers conclude from the chart that the income inequality problem in the U.S. is overblown. You just can't see it on that chart. That's because the chart literally hides this information. As we know, the top 20% of the U.S. population holds 84% of the wealth, and it gets worse with the top 1%, top 0.1%, etc. The precision of the horizontal axis of the chart is the "ventile", which are 5% buckets.

Also, notice that this type of chart is used to compare one distribution against another distribution. The notion of currencies has been entirely removed. It's similar to converting data from absolute units to rankings. You lose that sense of scale. (This is the reason why it appears as if no one in India makes more than anyone in the States. If a finer scale were to be used, at the upper end of the Indian income distribution, I'm sure you find otherwise.)